Mumbai City FC assistant coaches Marco Leite and Pedro Miguel Correia will also be leaving the club.
Clear-cut chances were few and far between in what was an intense contest that saw Mumbai City reduced to 10-men in the second half.
A recent change in coaching staff, with Clifford Miranda taking over as interim coach from Sergio Lobera, has made a positive impact on their on-field performance. FC Goa scored a convincing 4-1 win over Hyderabad FC in their last game.
A first-half goal from Diego Carlos (44') was all that Jorge Costa's men needed to notch an important win at home while NorthEast United went a fourth successive game without scoring.
Defensive mistakes cost Bengaluru dear and helped Mumbai's cause as Modou Sougou (13th) took advantage of Gurpreet Singh Sandhu's error to give his team the lead.
After starting the season with away fixtures and then playing a couple in Pune as their home stadium was getting ready, Josep Gombau's team have notched two home wins in a row at the Kalinga Stadium.
Mumbai registered their first 'home win' against laggards Hyderabad FC (2-1) when the two sides met at the Mumbai Football Arena last Sunday, with Modou Sougou scoring a brace.
The win takes Mumbai to the fourth spot, level on points with defending champions Bengaluru FC with 16 points. Hyderabad remain rooted to the bottom with a mere five points.
Before starting his media conference after Mumbai City FC's 3-2 win over Bengaluru FC on Sunday, Costa read out a statement, saying that referee Turki Alkhudhayr called Serge Kevyn a monkey and "made some gestures" which were disrespectful.
Michael Soosairaj gave the home side the lead against the run of play in the 39th minute, capitalising on a delightful through ball into the box by Edu Garcia.
The Guardiola-coached English Premier League champions Manchester City's parent company, City Football Group, have bought a majority 65 per cent stake in Indian Super League franchise Mumbai City FC.
Mumbai City FC co-owner and actor Ranbir Kapoor on Thursday expressed his delight at City Football Group (CFG) buying a 65% stake in the Indian Super League (ISL) side.
City Football Group will become the 65 per cent majority stakeholder of the club, alongside existing shareholders, actor Ranbir Kapoor and Bimal Parekh, who will keep the remaining 35 per cent.
Before this match, Mumbai had gone down 1-0 to Jamshedpur FC in an 'away' game and 2-0 to FC Goa in their previous home game.
Mumbai's unbeaten run of nine games ended when they suffered a 2-0 loss against FC Goa here at the Mumbai Football Arena in their previous home game.
After a goalless first half, Jamshedpur stepped up the pressure on Mumbai and found the match-winner through Memo in the 80th minute.
Edu Bedia and star striker Ferran Corominas struck on either side of the break at the Mumbai Football Arena to help FC Goa beat Mumbai City FC 2-0.
Mumbai and Bengaluru are on top of the league table with 27 points each, though Mumbai have played 13 matches, one more than the visitors.
The night belonged to Sougou, who scored in the 12th, 15th, 30th minute and second half injury time, as he made a mockery of Kerala's defence at the Mumbai Football Arena.
The victory sees Mumbai climb the fourth spot in the table, while Delhi Dynamos are rooted to the bottom without a win to their name.